Application of the finite-element-synthesis model to multidimensional reactor transient problems without feedback

The finite-element-synthesis model has been employed to solve time-dependent multigroup diffusion equations with multiple delayed-neutron precursor groups. Feedback effects are not considered. Precursor equations are analytically integrated within a time step, assuming linear variation of fission rate during the time interval. A fully implicit scheme is used for the time integration of the mixing functions. A coarse-mesh rebalancing technique is found to considerably accelerate the convergence of the inhomogeneous source problem of each time step. Many 2-D and 3-D problems were analysed with the present calculational model. The results are in good agreement with those of other less approximate methods, except for the problems in which the reflector zone is perturbed. There is a considerable saving in computer time due to the synthesis approximation.